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Schwarzschild metric
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Spacetime around a spherical mass.
The exact solution for the spacetime outside a spherical mass: ds² = −(1 − r_s/r)c²dt² + dr²/(1 − r_s/r) + r²dΩ². It predicts perihelion precession, light bending and black holes.
At r = r_s the coordinates are singular (horizon).
Only a coordinate singularity at r_s, real singularity at r = 0.
In more detail
The Schwarzschild metric describes spacetime outside a non-rotating spherical mass. It predicts gravitational time dilation, light bending and the event horizon of a black hole.
Real-world uses
- Models of stars and black holes use the Schwarzschild metric.
- It is used to compute orbits around compact objects.
- Physicists use the Schwarzschild solution to describe the spacetime around a non-rotating star or black hole.
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Frequently asked questions
Who found it?
Karl Schwarzschild, in 1916, shortly after Einstein's theory was published.
What does it predict?
A black hole horizon at the Schwarzschild radius.
What does the Schwarzschild solution describe?
The simplest exact solution of Einstein's equations, for a spherically symmetric, non-rotating mass.
Related topics in Relativity
Curved spacetime · Einstein field equations · Geodesics · Black hole event horizon · Hawking radiation · Gravitational waves detection